A new compact and low phase imbalance microstrip coupler for 5G wireless communication systems

Microstrip couplers play a crucial role in signal processing and transmission in various applications, including RF and wireless communication, radar systems, and satellites. In this work, a novel microstrip 180° coupler is designed, fabricated and measured. The layout configuration of this coupler is completely new and different from the previously reported Rat-race, branch-line and directional couplers. To obtain the proposed coupler, the meandrous coupled lines are used and analyzed mathematically. To improve the performance of our coupler, an optimization method is used. The designed coupler is very compact with an overall size of 0.014λg2. The obtained values of S21 and S31 are -3.45 dB and -3.75 dB, respectively at the operating frequency, while the fractional bandwidth (FBW) is 56.2%. It operates at fo = 1.61 GHz (suitable for 5G applications) and can suppress harmonics up to 2.17fo. Another advantage of this coupler is its low phase imbalance, while the phase difference between S21 and S31 is 180°± 0.023°. Therefore, our device is a balanced coupler with ±0.3 dB magnitude unbalance at its operating frequency. It is important to note that it is very difficult to find a coupler that has all these advantages at the same time. The proposed 180° coupler is fabricated and measured. The comparison shows that the measurement and simulation results are in good agreement. Therefore, the proposed coupler can be easily used in designing high-performance 5G communication systems.


Introduction
In modern microwave and RF communication systems, microstrip passive devices play a crucial role in signal processing and transmission.These devices include couplers, filters, splitters, and power dividers, among others.Microstrip passive devices are widely used due to their compact size, low cost, ease of fabrication, and excellent performance characteristics.They are used in various applications, such as in satellite communication, radar systems, wireless communication, and medical equipment.In recent years, the demand for high-performance microstrip passive devices has increased significantly due to the growing demand for wireless communication technologies such as 5G, Internet of Things (IoT), and autonomous vehicles [1][2][3][4][5][6][7][8][9].Therefore, the development of novel microstrip passive devices with improved performance characteristics is essential to meet the requirements of modern microwave/RF communication systems.Meanwhile, microstrip couplers with small sizes and high efficiency are attractive.Therefore, several types of them have been reported [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25].In [10], a microstrip branch-line coupler based on step impedance sections is designed.Two branch-line couplers using microstrip meandrous cells are designed in [11][12][13].The proposed coupler in [11] operates at 1.87 GHz for GSM applications.The common advantage of the designed couplers in [11,13] is their filtering frequency responses.However, the sizes of the reported couplers in [10][11][12][13] are large.The presented coupler in [14] is very compact with low phase imbalance.However, it does not has a filtering frequency response.The other microstrip couplers in [15][16][17][18][19][20][21][22][23][24][25] have large implementation areas, while all of them have high phase imbalances.The common weakness of the presented couplers in [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] is that their best values of S 21 and S 31 are not suitable in their passbands.Two microstrip couplers with arbitrary power divisions and filtering frequency response are designed in [15,16].However, they are not able to suppress harmonics correctly.In [17], using T-shape and open stubs a microstrip coupler is designed for 5G applications.In [18], a microstrip three-section branch-line coupler with a wideband is proposed.Interdigital cells are utilized in [19] to obtain a microstrip Rat-race coupler.Another Rat-race coupler using a microstrip spiral resonator is introduced in [20].To design a 3-dB branch-line coupler in [21], λ/4 open circuited coupled lines are used.The designed coupler in [22] is suitable for 5G applications, which has a simple structure.In this paper, the design of a microstrip 180˚coupler is presented to solve the problems of large size, high loss, phase imbalance and harmonics.The configuration of the proposed coupler is completely new and it is not similar to any previous coupler structures.It operates at 1.61 GHz, which is suitable for 5G applications.Our design method is based on a mathematical analysis of a novel resonator.Then, using the proposed resonator two bandpass filters (BPFs) are designed and integrated to obtain the proposed coupler.Additional optimizations are used to improve the frequency response.Finally, to verify the advantages of our coupler a complete comparison with the previous works is done.

Mathematical analysis of a new resonator
Thin coupled lines can create bandpass channels.Because these thin lines have inductive properties and also create some small capacitors.Accordingly, we proposed a novel bandpass resonator as shown in Fig 1 .Also, the approximated equivalent LC circuit and the simplified LC circuit of this resonator are depicted in Fig 1 .We ignored the effects of bents in the proposed LC circuit.This is because they are significant at frequencies higher than 10 GHz.Also, we used the approximated equivalent of the coupled lines.In the exact model, the number of coupling capacitors will be increased.The coupling capacitors are presented by C C1 and C C2 in Fig 1 .The inductor L 1 is an equivalent of the line with the physical length l 1 .Meanwhile the equivalents of the physical lengths l 2 and l 3 are the inductors L 2 and L 3 , respectively.Since there are some microstrip cells with the same physical dimensions, we used similar names for them.For clarity in Fig 1, the colors of the LC equivalent circuit are chosen to be the same as its corresponding physical structure.After that, the Δ to Y transform is used to simplify the presented LC circuit.The input impedance is calculated from the input port when the output port is open.
Where ω is an angular frequency.As can be seen, Z a is the impedance of an inductor.By comparing Fig 1(C) and 1(D), we can see that, the impedances Z 1 and Z 2 are the results of Δ to Y transformation, which will be obtained based on the values and locations of C C2 and L 2 .Therefore, the values of the impedances Z 1 and Z 2 can be calculated as follows: By considering the range of the coupling capacitor C C2 (C C2 has a very small value), the predetermined value of the operating frequency and the range of the inductor L 2 it can be seen that the impedance Z 1 belongs to an inductor.Also, as presented in Eq (2B), since Z 2 is a negative impedance it can be the impedance of a capacitor.As it can be seen in  impedance of the proposed resonator (Z in ) can be obtained by: According to the predetermined value of the resonance frequency and also the range of lumped elements, some terms are very small compared to the others.Therefore, the small terms can be removed with a good approximation.Our target frequency is in the GHz range and the inductors are in nH.The simulation results show that the coupling capacitors usually have small values in pF (or fF).Accordingly, to find the resonator behavior we can use the following approximation: Based on Eq (4) and the above explanations about the range of lumped elements, Eq (3) can be simplified as follows: To find the operating frequency, we can set Z in = 0. Therefore, based on the approximated value of Z in in Eq (5) we can obtain the resonance condition as follows: By setting the numerator of Eq (5) equal to zero, Eq (6) can be obtained where ω 1 is the operating frequency of the proposed resonator.Based on the range of inductors, capacitors and angular frequency, the following approximations can be applied in Eq (6): The above approximations are acceptable for the small coupling capacitor (C C2 is in fF or pF ranges), the inductor in nH, where ω 1 can be a resonance frequency or a harmonic in GHz.Since Eq (7) is not reasonable, we conclude that the resonance frequency can occur when Z in = 1.This is an advantage.Because if we have two resonance frequencies, one of them is a harmonic (ω 1 ) that must be removed.But our proposed structure removes this harmonic by itself.For Z in = 1, we can write that: ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffiffi Where ω 2 is the operating frequency of the proposed resonator.Based on Eq (8), the values of inductors and capacitors can be adjusted for a predetermined angular frequency.By adjusting these values, the dimensions of the transmission lines and the distance between the coupled lines can be found.Therefore, it is possible to simultaneously reduce the dimensions and adjust the operating frequency using Eq (8).Using the presented mathematical analysis and calculated angular frequencies, the behavior of the basic resonator is specified and as a result the optimization of the final layout can be done more easily.Based on Eq (8), for a predetermined target resonance frequency, we have a high degree of freedom to choose inductors and coupling capacitors.After choosing them, we can calculate the physical dimensions using the Richard transformations.However, the exact dimensions will be determined after applying the optimization method and changing the important dimensions extracted by the presented mathematical analysis and equations.Using Eq (8), the resonator behavior can be determined.Then we can optimize the dimensions accordingly.For example, the resonance frequency can be determined beforehand.Then, the values of the inductors can be changed in such a way that the least possible space is occupied.A method is reducing the distance between coupled lines to reduce the insertion loss.However, we should be careful not to increase the harmonics by reducing the gap between coupled lines.Then, for two predetermined values of the resonance frequency and the coupling capacitor, the inductors can be determined using the optimization method.According to Eq (8), by increasing an inductor, the operating frequency moves to the left.Therefore, increasing the physical lengths presented in Fig 1(A) (l 1 , 2l 2 , and 2l 3 ), shifts the resonance frequency to the left.Using the analyzed resonator and additional optimizations, two bandpass filters (BPFs) i.e.BPF1 and BPF2 are designed.

Design and analysis of a novel coupler
The layouts and frequency responses of BPF1 and BPF2 are shown in Fig 2, where all dimensions are in mm.A Rogers RT/Duroid5880 substrate with ε r = 2.22, tan (δ) = 0.0009 and h = 31 mil is used to design these BPFs.The insertion loss of BPF1 is 0.27 dB at 1.77 GHz, while for BPF2 the insertion loss is 1.2 dB at 1.58 GHz.Since the resonant frequencies are close to each other, these BPFs can be integrated to design a microstrip coupler.During the integration, additional microstrip cells can be added to the coupler structure to improve the frequency response.After obtaining the proposed filters, we must connect them to each other and add the isolation port (Port 4).The function of this port can be controlled by our optimization method.The layout of the proposed coupler with a photograph of the fabricated structure are presented in Fig 3, where all dimensions are in mm.Also, all widths of the thin lines are 0.1 mm.Since our coupler consists of two designed filters.First, we designed two BPFs.Then, we integrated them to achieve our coupler.We didn't change the dimensions of these filters in the coupler structure.After integrating the proposed BPFs, we added some transition lines (TLs) to the final layout.Reducing the distance between these cells and the main body of the BPFs causes the loading effect.Therefore, we set most of these spaces equal or greater than 0.2 mm.However, their coupling effects are not always negative.Because the simulation results show that, they can improve the return loss somewhat.Since our proposed device is a -3dB coupler, the values of S 21 and S 31 at the intersection point is higher than the designed BPFs.However, the best values of S 21 and S 31 at the passband are low similar to the BPFs.These filters form the main body of the proposed coupler.Therefore, we focused on designing the presented filters to reach the proposed coupler.This method can be used to design other microstrip filtering devices, which is presented for the first time in this work.The overall size of this coupler is 20.1 mm×14.8mm = 0.14λ g × 0.103λ g , where λ g is the guided wavelength calculated at the operating frequency.The used substrate is a Rogers RT/Duroid 5880 with ε r = 2.22, tan (δ) = 0.0009 and h = 31 mil.Four loaded solid rectangles are added on a 0.1 mm thin transmission line between BPF1 and BPF2.This structure plays a role in smoothing the passband as well as suppressing some harmonics.Ports 1 and 4 are connected by ten small solid rectangles loaded on another thin transmission line.This coupler uses a novel curved coupling line as a resonator, which is presented for the first time in this work.
To find the important parameters and to facilitate the optimization, the current density distributions (at 1.6 GHz) for the excitation of ports 2 and 3 are shown in  To shift S 21 to the left and improve the losses, we can increase l 4 and reduce S 1 respectively.Another way for shifting S 21 to the left is increasing the width w 2 , while tuning w 1 has more impact on the loss at port 2. Fig 6 shows the design steps for the proposed coupler.As shown in this figure, after designing the resonator we obtained two BPFs.Next, we integrated them in such a way that the final structure occupies the least possible space.An additional slotted line and some rectangular shapes are added after connecting the presented BPFs.These cells are added to improve the isolation factor.All of the rectangular cells have capacitor feature where they are shunt.When they are placed next to the thin lines with the inductor feature, a lowpass frequency response is created (the stopband of this lowpass filter is located on the passband of our coupler).Accordingly, we can create an isolation port.

Simulation and measurement results
The simulation results are obtained by the EM simulator of Advanced Design Systems software.The measurement results are obtained by an HP8757A network analyzer.The simulation and measurement results are close to each other.However, due to having copper and terminal losses the measured losses are a little higher than the simulations losses.The simulated and measured S-Parameters and phase difference between S 21 and S 31 are presented in Fig 7.
The operating frequency of this coupler is located at f o = 1.611GHz, where the phase difference between S 21 and S 31 is only 0.023˚at this frequency.The obtained values of S 21 and S 31 are -3.45dB and -3.75 dB, respectively.There are several transmission poles in S 11 and S 41 (at the passband), which the best values of them are -19.67 dB and -33.99 dB, respectively.In the passband, the best values of S 31 and S 21 are -2.275dB and -2.108 dB, respectively (located at two difference frequencies).However, the magnitude imbalance at the passband is below ±3.5 dB.For the values of S 11 better than -10 dB, the fractional bandwidth (FBW) is 56.1%.Also, from 1.1 GHz to 2.3 GHz both S 21 and S 31 are higher than -6 dB.Therefore, the -6dB FBW is near 75%.The phase imbalance from 1.53 GHz to 1.67 GHz is below 10º while near the operating frequency from 1.58 GHz to 1.64 GHz the phase imbalance value is below 5º.The harmonics are suppressed up to 3.5 GHz with a maximum harmonic level of -15.7 dB.The value of S 11 is better than -10 dB from 1.189 GHz to 2.07 GHz, where the magnitude imbalance at this frequency range is better than ±3.5 dB.This frequency range is suitable for mid-band 5G applications, which covers 1-6 GHz frequency range.

Comparison with the previous works
To verify the advantages of the proposed coupler, we compared it with the previously reported couplers as shown in Table 1.From this table it is clear that the best values of S 21, S 31 and FBW % are obtained in this work.Moreover, our coupler size and phase imbalance are very small.Only the proposed coupler in [14] is smaller than our coupler.However, it does not have a By comparing the equivalent circuits shown in Fig 1(B) and 1(C), it can be seen that the impedance Z a is the sum of the impedances L 1 , L 2 and L 3 .Therefore, in Fig 1, after simplification of the LC circuit the values of the impedance Z a is: Fig 1(D), The input

Fig 4 .
Also, the significant physical length and widths are specified in Fig 4.As can be seen, the thin lines have more current densities.Fig 5 depicts the frequency response as functions of nine significant parameters shown in Fig 4. The proposed filters have loading effects after connecting.To reduce the negative effects and improve the frequency response, the rectangular cells are added to the final layout.These cells have capacitive characteristics and their dimensions are selected by the

Fig 5 .
Fig 5. Frequency response of the proposed coupler as functions of the significant parameters, the effect of changing.(a) l 1 on S 21 and S 31 , (b) l 2 on S 21 and S 31 , (c) l 3 on S 21 and S 31 , (d) l 4 on S 21 and S 31 , (e) l 5 on S 21 and S 31 , (f) l 6 on S 21 and S 31 , (g) S 1 on S 21 and S 31 , (h) w 1 on S 21 and S 31 , (i) w 2 on S 21 and S 31 .https://doi.org/10.1371/journal.pone.0296272.g005